A heavy rope is suspended from a rigid support. A wave pulse is set up at the lowerend, then :a)the pulse will travel with decreasing speedb)the pulse will travel with increasing speedc)the pulse will travel with uniform speedd)the pulse cannot travel through the ropeCorrect answer is option 'B'. Can you explain this answer?

Question

Answer

Explanation:

When a wave pulse is set up at the lower end of a heavy rope suspended from a rigid support, the pulse will travel with increasing speed. This can be understood by considering the properties of wave propagation and the behavior of a heavy rope.

Wave Propagation:
When a wave travels through a medium, it transfers energy without transporting matter. The speed of a wave depends on the properties of the medium through which it travels. In the case of a heavy rope, the speed of the wave pulse depends on the tension in the rope and the mass per unit length of the rope.

Behavior of a Heavy Rope:
In a heavy rope, the tension is greater at the top and decreases towards the bottom due to the weight of the rope. The mass per unit length of the rope is also greater at the top and decreases towards the bottom.

Explanation of Option B:
The wave pulse in the heavy rope will travel with increasing speed because of the decreasing tension and mass per unit length towards the bottom of the rope. Here is a detailed explanation:

1. At the lower end of the rope, where the wave pulse is set up, the tension and mass per unit length are relatively smaller compared to the top of the rope.
2. As the wave pulse travels upwards, it encounters regions of higher tension and mass per unit length.
3. Due to the higher tension and mass per unit length, the wave pulse experiences a greater resistance to motion, causing it to slow down initially.
4. However, as the wave pulse moves further up, it encounters regions of lower tension and mass per unit length.
5. The lower tension and mass per unit length result in less resistance to motion, allowing the wave pulse to accelerate.
6. Therefore, the wave pulse travels with increasing speed as it moves towards the top of the rope.

Conclusion:
In conclusion, the wave pulse will travel with increasing speed in a heavy rope suspended from a rigid support. This is due to the variation in tension and mass per unit length along the length of the rope.

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